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Journal Articles

The Approximate Analysis of Higher-Order Frequencies of Nonlinear Vibrations of a Cantilever Beam With the Extended Galerkin Method

Baochen Meng, Chencheng Lian, Ji Wang, Huimin Jing, Rongxing Wu, Ji Lin, Isaac Elishakoff
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. April 2024, 19(4): 041005.
Paper No: CND-23-1263
https://doi.org/10.1115/1.4064724
Published Online: February 29, 2024
View Article titled, The Approximate Analysis of Higher-Order Frequencies of Nonlinear Vibrations of a Cantilever Beam With the Extended Galerkin Method
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Topics: Cantilever beams, Rotation, Vibration, Galerkin method, Mode shapes
Journal Articles

Floquet Theory for Linear Time-Periodic Delay Differential Equations Using Orthonormal History Functions

Junaidvali Shaik, Sankalp Tiwari, C. P. Vyasarayani
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. September 2023, 18(9): 091005.
Paper No: CND-23-1017
https://doi.org/10.1115/1.4062633
Published Online: June 14, 2023
View Article titled, Floquet Theory for Linear Time-Periodic Delay Differential Equations Using Orthonormal History Functions
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Topics: Delay differential equations, Delays, Stability, Galerkin method
Journal Articles

An Alternative Formulation for Modeling Self-Excited Vibrations of Drillstring With Polycrystalline Diamond Compact Bits

Kaixiao Tian, Emmanuel Detournay, He Zhang
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. May 2022, 17(5): 051002.
Paper No: CND-21-1308
https://doi.org/10.1115/1.4053407
Published Online: March 8, 2022
View Article titled, An Alternative Formulation for Modeling Self-Excited Vibrations of Drillstring With Polycrystalline Diamond Compact Bits
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Topics: Delays, Drill strings, Equations of motion, Galerkin method, Modeling, Polycrystalline diamond compact bits, Rocks, Stability, Torque, Trajectories (Physics)
Journal Articles

Computing Natural Frequencies and Mode Shapes of an Axially Moving Nonuniform Beam

Alok Sinha
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. April 2022, 17(4): 041001.
Paper No: CND-21-1197
https://doi.org/10.1115/1.4053271
Published Online: January 13, 2022
View Article titled, Computing Natural Frequencies and Mode Shapes of an Axially Moving Nonuniform Beam
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Topics: Boundary-value problems, Mode shapes, Partial differential equations, Eigenvalues, Galerkin method, Optimization, Time-varying systems
Journal Articles

Pole Placement for Delay Differential Equations With Time-Periodic Delays Using Galerkin Approximations

Shanti Swaroop Kandala, Thomas K. Uchida, C. P. Vyasarayani
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. September 2021, 16(9): 091007.
Paper No: CND-20-1378
https://doi.org/10.1115/1.4051590
Published Online: July 27, 2021
View Article titled, Pole Placement for Delay Differential Equations With Time-Periodic Delays Using Galerkin Approximations
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Topics: Delay differential equations, Delays, Galerkin method, Pendulums, Stability, Pole placement, Feedback, Optimization, Time delay systems
Journal Articles

Discontinuous Galerkin Method and Dual-SLERP for Time Integration of Flexible Multibody Dynamics

Shilei Han, Olivier A. Bauchau
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. September 2020, 15(9): 091003.
Paper No: CND-19-1419
https://doi.org/10.1115/1.4046736
Published Online: July 16, 2020
View Article titled, Discontinuous Galerkin Method and Dual-SLERP for Time Integration of Flexible Multibody Dynamics
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Topics: Equations of motion, Errors, Galerkin method, Interpolation, Multibody dynamics, Multibody systems, Rotation, Tensors, Displacement, Buckling
Journal Articles

A Mechanical Model Based on Conformal Strain Energy and Its Application to Bending and Buckling of Nanobeam Structures

Zaher Rahimi, Wojciech Sumelka, Dumitru Baleanu
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. June 2019, 14(6): 061004.
Paper No: CND-18-1376
https://doi.org/10.1115/1.4043085
Published Online: April 8, 2019
View Article titled, A Mechanical Model Based on Conformal Strain Energy and Its Application to Bending and Buckling of Nanobeam Structures
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Topics: Buckling, Galerkin method
Journal Articles

Wavelets Galerkin Method for the Fractional Subdiffusion Equation

M. H. Heydari
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. November 2016, 11(6): 061014.
Paper No: CND-15-1114
https://doi.org/10.1115/1.4034391
Published Online: August 22, 2016
View Article titled, Wavelets Galerkin Method for the Fractional Subdiffusion Equation
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Topics: Algebra, Algorithms, Boundary-value problems, Diffusion (Physics), Errors, Galerkin method, Linear systems, Wavelets, Numerical analysis
Journal Articles

Jacobi Spectral Galerkin and Iterated Methods for Nonlinear Volterra Integral Equation

Yin Yang, Yanping Chen
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. July 2016, 11(4): 041027.
Paper No: CND-15-1073
https://doi.org/10.1115/1.4033439
Published Online: May 24, 2016
View Article titled, Jacobi Spectral Galerkin and Iterated Methods for Nonlinear Volterra Integral Equation
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Topics: Errors, Galerkin method, Volterra equations, Theorems (Mathematics)
Journal Articles

Stability of Human Balance With Reflex Delays Using Galerkin Approximations

Zaid Ahsan, Thomas K. Uchida, Akash Subudhi, C. P. Vyasarayani
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. July 2016, 11(4): 041009.
Paper No: CND-15-1080
https://doi.org/10.1115/1.4031979
Published Online: December 10, 2015
View Article titled, Stability of Human Balance With Reflex Delays Using Galerkin Approximations
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Topics: Pendulums, Stability, Galerkin method, Delays
Journal Articles

Galerkin Approximations for Stability of Delay Differential Equations With Distributed Delays

Anwar Sadath, C. P. Vyasarayani
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. November 2015, 10(6): 061024.
Paper No: CND-14-1269
https://doi.org/10.1115/1.4030153
Published Online: November 1, 2015
View Article titled, Galerkin Approximations for Stability of Delay Differential Equations With Distributed Delays
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Topics: Galerkin method, Stability, Delays, Delay differential equations
Journal Articles

Galerkin Approximations for Stability of Delay Differential Equations With Time Periodic Delays

Anwar Sadath, C. P. Vyasarayani
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. November 2015, 10(6): 061008.
Paper No: CND-14-1124
https://doi.org/10.1115/1.4028631
Published Online: November 1, 2015
View Article titled, Galerkin Approximations for Stability of Delay Differential Equations With Time Periodic Delays
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Topics: Delay differential equations, Delays, Galerkin method, Stability
Journal Articles

Galerkin Approximations for Stability of Delay Differential Equations With Time Periodic Coefficients

Anwar Sadath, C. P. Vyasarayani
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. March 2015, 10(2): 021011.
Paper No: CND-13-1298
https://doi.org/10.1115/1.4026989
Published Online: March 1, 2015
View Article titled, Galerkin Approximations for Stability of Delay Differential Equations With Time Periodic Coefficients
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Topics: Delays, Feedback, Galerkin method, Stability, Delay differential equations, Computer simulation
Journal Articles

Numerical Stability Analysis of Linear Incommensurate Fractional Order Systems

Sambit Das, Anindya Chatterjee
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. October 2013, 8(4): 041012.
Paper No: CND-12-1196
https://doi.org/10.1115/1.4023966
Published Online: May 31, 2013
View Article titled, Numerical Stability Analysis of Linear Incommensurate Fractional Order Systems
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Topics: Matlab, Numerical stability, Polynomials, Stability, Galerkin method, Eigenvalues, Computation
Journal Articles

Galerkin Approximations for Neutral Delay Differential Equations

C. P. Vyasarayani
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. April 2013, 8(2): 021014.
Paper No: CND-12-1001
https://doi.org/10.1115/1.4007446
Published Online: October 1, 2012
View Article titled, Galerkin Approximations for Neutral Delay Differential Equations
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Topics: Delay differential equations, Galerkin method, Scalars
Journal Articles

Numerical Analysis of Panel Flutter on Inertial Manifolds With Delay

Guanhua Mei, Jiazhong Zhang, Zhuopu Wang
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research-Article
J. Comput. Nonlinear Dynam. April 2013, 8(2): 021009.
Paper No: CND-12-1031
https://doi.org/10.1115/1.4006948
Published Online: July 23, 2012
View Article titled, Numerical Analysis of Panel Flutter on Inertial Manifolds With Delay
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Topics: Delays, Flutter (Aerodynamics), Galerkin method, Manifolds, Oscillations, Numerical analysis, Deformation
Journal Articles

Galerkin Approximations for Higher Order Delay Differential Equations

C. P. Vyasarayani
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research Papers
J. Comput. Nonlinear Dynam. July 2012, 7(3): 031004.
https://doi.org/10.1115/1.4005931
Published Online: March 19, 2012
View Article titled, Galerkin Approximations for Higher Order Delay Differential Equations
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Topics: Delay differential equations, Galerkin method
Journal Articles

Ritz Legendre Multiwavelet Method for the Damped Generalized Regularized Long-Wave Equation

S. A. Yousefi, Z. Barikbin
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Technical Briefs
J. Comput. Nonlinear Dynam. January 2012, 7(1): 014501.
https://doi.org/10.1115/1.4004121
Published Online: July 22, 2011
View Article titled, Ritz Legendre Multiwavelet Method for the Damped Generalized Regularized Long-Wave Equation
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Topics: Approximation, Boundary-value problems, Galerkin method, Polynomials, Wavelets, Waves, Algebra, Function approximation, Nonlinear differential equations, Numerical analysis
Journal Articles

Modeling MEMS Resonators Past Pull-In

Chandrika P. Vyasarayani, Eihab M. Abdel-Rahman, John McPhee, Stephen Birkett
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research Papers
J. Comput. Nonlinear Dynam. July 2011, 6(3): 031008.
https://doi.org/10.1115/1.4002835
Published Online: February 1, 2011
View Article titled, Modeling MEMS Resonators Past Pull-In
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Topics: Dynamic response, Galerkin method, Microelectromechanical systems, Mode shapes, Modeling, Springs, Switches, Deflection, Electrodes, Eigenvalues
Journal Articles

Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems

Satwinder Jit Singh, Anindya Chatterjee
Journal: Journal of Computational and Nonlinear Dynamics
Publisher: ASME
Article Type: Research Papers
J. Comput. Nonlinear Dynam. April 2011, 6(2): 021010.
https://doi.org/10.1115/1.4002516
Published Online: October 28, 2010
View Article titled, Unified Galerkin- and DAE-Based Approximation of Fractional Order Systems
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Topics: Approximation, Stability, Differential algebraic equations, Galerkin method